# Adiabatic following of an induced dipole moment

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Hello! Assume I have a 2 level system, where the 2 levels have opposite parity. If I apply an electric field, I will get an induced dipole moment. For now I want to keep it general, so the induced dipole moment can be very large, too. Let's say that I start rotating this electric field in the x-y plane, such that the field is given by:

$$E(t) = E_0(\cos{(\omega t)}\hat{x} + \sin{(\omega t)}\hat{y} )$$

I want to describe the behavior of the dipole in the lab frame. I assume that for small rotation frequencies, $\omega$, I am in an adiabatic regime and the dipole would follow the electric field, while at high frequencies, the dipole would not be able to follow. However, I am not sure how to derive these in practice starting from the Hamiltonian. Also, I am not sure what we mean by small/large frequencies in this case. Would I need to compare to the spacing between the 2 levels of opposite parity, or with the Rabi frequency of the field i.e. $dE_0$ where $d$ is the matrix element between the 2 levels of opposite parity. Can someone help me with this, or point me towards some derivations? Thank you!

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